multissim3

Multiscale structural similarity (MS-SSIM) index for volume quality

Description

example

score = multissim3(V,Vref) calculates the multiscale structural similarity (MS-SSIM) index, score, for volume V, using Vref as the reference volume.

The 3-D MS-SSIM operation is defined for grayscale volumes. For inputs with more than three dimensions, multissim3 treats each element of higher dimensions as separate 3-D grayscale volumes. multissim3 treats 2-D RGB images as 3-D grayscale volumes. To calculate the MS-SSIM of color channels in an RGB image, use the multissim function.

example

score = multissim3(V,Vref,Name,Value) controls aspects of the computation using one or more name-value arguments. For example, specify the number of scales using the 'NumScales' argument.

example

[score,qualityMaps] = multissim3(___) also returns the local MS-SSIM index value for each voxel in V, and each of the scaled versions of V. The qualityMaps output is a cell array containing maps for each of the scaled versions of V, with each quality map the same size as the corresponding scaled version.

Examples

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Load a 3-D volume into the workspace.

Vref = squeeze(D);

Create a noisy version of the original volume for quality measurement comparison purposes.

V = imnoise(Vref,'salt & pepper',0.05);

Calculate the MS-SSIM index that measures the quality of the input volume compared to the reference volume.

score = multissim3(V,Vref)
score = single
0.7261

Load a volume into the workspace. This volume will be the reference volume. Create a copy of the reference volume.

Vref = squeeze(D);
V = Vref;

Add noise to a localized part of the volume for quality comparison purposes.

V(1:100,1:100,1:10) = imnoise(Vref(1:100,1:100,1:10),'salt & pepper',0.05);
figure
sliceViewer(V); Calculate the MS-SSIM index for the volumes and retrieve the local structural similarity maps. The multissim3 function returns qualitymaps, a cell array containing a local structural similarity map for each of the scaled versions of the volume. In the quality map, the value 1 indicates the highest quality.

[score, qualitymaps] = multissim3(V,Vref);
figure
sliceViewer(V); Load a volume into the workspace.

Vref = squeeze(D);

Create a noisy version of the volume for quality measurement comparison purposes.

V = imnoise(Vref,'salt & pepper',0.05);

Calculate the MS-SSIM index for the noisy volume, using the original volume as the reference. Specify how much to weigh the local MS-SSIM index calculations for each scaled volume using the 'ScaleWeights' argument. The example uses the weights defined in the article by Wang, Simoncelli, and Bovik.

score = multissim3(V,Vref,'ScaleWeights',[0.0448,0.2856,0.3001,0.2363,0.1333]);

Read a volumetric image into the workspace.

VRef = im2single(VRef.mristack);

Simulate a batch of six images by replicating the image along the fourth dimension.

VRefBatch = repmat(VRef,[1 1 1 6]);

Create a version of the image stack with added salt and pepper noise.

VNoisyBatch = imnoise(VRefBatch,"salt & pepper");

Calculate the MS-SSIM of each volume in the stack.

score = multissim3(VNoisyBatch,VRefBatch)
score = 1x1x1x6 single array
score(:,:,1,1) =

0.8341

score(:,:,1,2) =

0.8347

score(:,:,1,3) =

0.8337

score(:,:,1,4) =

0.8333

score(:,:,1,5) =

0.8348

score(:,:,1,6) =

0.8343

Read a volumetric image into the workspace.

VRef = im2single(VRef.mristack);

Create a copy of the batch of images, adding salt and pepper noise.

Vnoisy = imnoise(VRef,"salt & pepper");

Create unformatted dlarray objects for the original and noisy batch of images.

dlref = dlarray(VRef);
dlnoisy = dlarray(Vnoisy);

Calculate the MS-SSIM score of the noisy data with respect to the original data.

score = multissim3(dlnoisy,dlref)
score =
1x1 single dlarray

0.8341

Input Arguments

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Input volume, specified as a numeric array of three or more dimensions or a dlarray (Deep Learning Toolbox) object. Formatted dlarray objects cannot include more than one channel label, more than one batch label, and more than three spatial labels.

Data Types: single | double | int16 | uint8 | uint16

Reference volume, specified as a numeric array of three or more dimensions or a dlarray (Deep Learning Toolbox) object. Formatted dlarray objects cannot include more than one channel label, more than one batch label, and more than three spatial labels. The reference volume must be of the same size and data type as the input volume, V.

Data Types: single | double | int16 | uint8 | uint16

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: score = multissim3(V,Vref,'NumScales',3);

Number of scales used to calculate MS-SSIM, specified as the comma-separated pair consisting of 'NumScales' and a positive integer. Setting 'NumScales' to 1 is equivalent to the use of the ssim function with the 'Exponents' name-value pair argument set to [1 1 1]. The size of the input volume limits the number of scales. The multissim3 function scales the volume (NumScales - 1) times, downsampling the volume by a factor of 2 with each scaling.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Relative values across the scales, specified as the comma-separated pair consisting of 'ScaleWeights' and a vector of positive numbers. The length of the vector is equal to the number of scales, because each element corresponds to one of the scaled versions of the original volume. The multissim3 function normalizes the values to 1. By default, the scale weights equal fspecial('gaussian',[1,numScales],1). The multissim3 function uses a Gaussian distribution as the default because the human visual sensitivity peaks at middle frequencies and decreases in both directions. For an example of setting 'ScaleWeights', see Calculate MS-SSIM Specifying Weights for Each Scaled Volume.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Standard deviation of the isotropic Gaussian function, specified as the comma-separated pair consisting of 'Sigma' and a positive number. This value specifies the weighting of the neighborhood voxels around a voxel for estimating local statistics. The multissim3 function uses this weighting to avoid blocking artifacts in estimating local statistics.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Dynamic range of the input volume, specified as a positive number. The default value of DynamicRange depends on the data type of volume V, and is calculated as diff(getrangefromclass(V)). For example, the default dynamic range is 255 for volumes of data type uint8, and the default is 1 for volumes of data type double or single with voxel values in the range [0, 1].

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Output Arguments

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MS-SSIM index for image quality, returned as a numeric scalar, numeric array, or dlarray (Deep Learning Toolbox) object as indicated in the table. The value of score is typically in the range [0, 1]. The value 1 indicates the highest quality and occurs when V and Vref are equivalent. Smaller values correspond to poorer quality. For some combinations of inputs and name-value pair arguments, score can be negative.

Input Volume TypeMS-SSIM Value
3-D numeric matricesNumeric scalar with a single MS-SSIM measurement.
3-D dlarray objects1-by-1 dlarray object with a single MS-SSIM measurement.
N-D numeric arrays with N>3Numeric array of the same dimensionality as the input volumes. The first three dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along the higher dimensions.

Unformatted N-D dlarray objects with N>3

dlarray object of the same dimensionality as the input volumes. The first three dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along the higher dimensions.

Formatted N-D dlarray objects with N>3

dlarray object of the same dimensionality as the input volumes. The spatial dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along any channel or batch dimension.

Local MS-SSIM index values for each pixel in each scaled version, returned as a cell array of numeric arrays or a cell array of dlarray (Deep Learning Toolbox) objects. The size of the cell array is 1-by-NumScales. Each element in qualityMaps indicates the quality of the corresponding pixel at the corresponding scale factor. The format of each element uses the formatting of the score argument, based on the format of the input volumes.

Algorithms

The structural similarity (SSIM) index measures perceived quality by quantifying the structural similarity between a volume and a reference volume (see ssim). The multissim3 function calculates the MS-SSIM by combining the SSIM index of several versions of the volume at various scales. The MS-SSIM index can be more robust when compared to the SSIM index with regard to variations in viewing conditions.

The multissim3 function uses double-precision arithmetic for input volumes of class double. All other types of input volumes use single-precision arithmetic.

 Wang, Z., Simoncelli, E.P., Bovik, A.C. Multiscale Structural Similarity for Image Quality Assessment. In: The Thirty-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, 1398–1402. Pacific Grove, CA, USA: IEEE, 2003. https://doi.org/10.1109/ACSSC.2003.1292216.